Comparing phylogenetic signal in intraspecific and interspecific body size datasets

Phylogenetic comparative methods have become a standard statistical approach for analysing interspecific data, under the assumption that traits of species are more similar than expected by chance (i.e. phylogenetic signal is present). Here I test for phylogenetic signal in intraspecific body size datasets to evaluate whether intraspecific datasets may require phylogenetic analysis. I also compare amounts of phylogenetic signal in intraspecific and interspecific body size datasets. Some intraspecific body size datasets contain significant phylogenetic signal. Detection of significant phylogenetic signal was dependant upon the number of populations (n) and the amount of phylogenetic signal (K) for a given dataset. Amounts of phylogenetic signal do not differ between intraspecific and interspecific datasets. Further, relationships between significance of phylogenetic signal and sample size and amount of phylogenetic signal are similar for intraspecific and interspecific datasets. Thus, intraspecific body size datasets are similar to interspecific body size datasets with respect to phylogenetic signal. Whether these results are general for all characters requires further study.     

Bias in interspecific allometry: examples from morphological scaling in varanid lizards

The traditional approach to allometric analysis entails the fitting of a straight line to logarithmic transformations of the data, after which parameters in a two-parameter allometric equation are estimated by back-transformation to the original scale. We re-examined published data for dimensions of the limbs in 22 species of varanid lizards to illustrate the biases that can be introduced into allometric analyses by applying the aforementioned protocol. Statistical models fit to the original data by linear and nonlinear regression conformed better with underlying assumptions than did models obtained by back-transformation from logarithms, and the former generally were better than the latter for describing limb dimensions over the full range in body size. Allometric exponents estimated by the traditional method therefore were based on inappropriate and inaccurate statistical models and, consequently, were biased and misleading. Investigators can avoid problems such as these by performing preliminary graphical and statistical analyses on data in their original scale and by validating the fitted model. Logarithmic transformations should be used sparingly and only for cause.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society , 2009, 96 , 296–305.     

Lumbar ontogenetic allometry and dimorphism in humans. A case for comparison between interspecific and intraspecific scaling

The ontogenetic allometry of the lumbar region of 1913 humans (1228 females and 685 males), ranging from newborn to 21-year-old individuals, was studied by means of length, width, projected surface area and bone mineral density of the segment L2 - L4, obtained by dual X-ray absorptiometry (DXA). All these parameters were regressed to body mass and height of the individuals, considered alternatively as the independent variable. Firstly, we addressed the comparison between the results obtained on both sexes in order to elucidate whether ontogenetic differences existed. Length of the segments increased significantly faster in females than in males, independently whether the regression was made against body mass or height, while in both types of regression width scaled in males faster than in females. Regarding bone mineral density, although males increased bone mineral density faster than females, slope differences were not significant. However, y-interception was significantly higher in females than in males when bone mineral density was regressed to body mass. Results on length and width are compared with others from previous research on allometry. Finally, global results are discussed as regards the slope predictions for interspecific scaling.     

A nondestructive method of calculating the wing area of insects

Most insects engage in winged flight. Wing loading, that is, the ratio of body mass to total wing area, has been demonstrated to reflect flight maneuverability. High maneuverability is an important survival trait, allowing insects to escape natural enemies and to compete for mates. In some ecological field experiments, there is a need to calculate the wing area of insects without killing them. However, fast, nondestructive estimation of wing area for insects is not available based on past work. The Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, is frequently used to calculate leaf area of plants, in crops with entire linear, lanceolate leaves. Recently, the ME was proved to apply to leaves with more complex shapes from plants that do not have any needle leaves. Given that the wings of insects are similar in shape to broad leaves, we tested the validity of the ME approach in calculating the wing area of insects using three species of cicadas common in eastern China. We compared the actual area of the cicadas’ wings with the estimates provided by six potential models used for wing area calculation, and we found that the ME performed best, based on the trade‐off between model structure and goodness of fit. At the species level, the estimates for the proportionality coefficients of ME for three cicada species were 0.686, 0.693, and 0.715, respectively. There was a significant difference in the proportionality coefficients between any two species. Our method provides a simple and powerful approach for the nondestructive estimation of insect wing area, which is also valuable in quantifying wing morphological features of insects. The present study provides a nondestructive approach to estimating the wing area of insects, allowing them to be used in mark and recapture experiments.     

Static intraspecific maxillofacial allometry in the chacma baboon

Adult static intraspecific allometry of jaw size and tooth area was evaluated in a sample of 104 Papio ursinus crania (52 male, 52 female). Tooth areas were calculated from mesiodistal and buccolingual measurements of all the teeth in both arcades and were scaled to four viscerocranial measurements: bimaxillary width, maxillo-alveolar length, mandibular length and bigonial width. Craniodental allometric analyses indicate that larger animals will tend to have proportionately shorter and narrower lower jaws. From the log-transformed interspecific analyses between P. ursinus and C. aethiops we conclude that males and females within each species share a common exponential value for jaw length. Hence increased sexual dimorphism for muzzle length in P. ursinus is attributable to increased divergence between the male and female slopes. Post-canine area was found to be significantly correlated to maxillary length and to canine size only in females, with exponential values similar to those reported for the same bivariate regressions in C. aethiops. A hypothesis of nutritional equivalence is advanced to account for these observations. Canine base area and the area of P3 were the only tooth areas that scaled in a positively allometric fashion to jaw size--but only in males. Hence the existence of a canine complex is confirmed in the male Chacma baboon, the size of which is related to jaw length.     

Information and allometry

Many life-history parameters have condition-dependent optima, but individuals are often required to set the values of such parameters relatively early in development, before the relevant conditions can be assessed with full accuracy. If cues are available that predict such future conditions, then the condition-dependent parameter should evolve to assume values that deviate from the mean in the direction implied by the cues, but these deviations should regress towards the mean to the degree that the cues are less than fully reliable. Under mild assumptions, the slopes of the resulting relationships between condition-dependent life-history parameters and the variable conditions on which their optima depend will be the ideal slopes (those that would maximize fitness if the parameter could be chosen on the basis of full information) devalued by the squared correlation between the condition and the parameter.     

Evidence for intraspecific phenotypic variation in songbirds along elevation gradients in central Europe

Studying phenotypic variations along gradients may provide insights into mechanisms that drive species distributions and thus can be useful indicators of environmental change. In mountains, the study of phenotypic variation along elevation gradients is of increasing relevance due to the impacts of climate change. We analysed European ringing data to measure the direction of phenotypic variation along elevation gradients in six common, resident songbird species occurring along a wide elevational range. We modelled intraspecific change in wing length, body mass and their ratio with elevation and found a significant increase in wing length and a decrease in body mass at high elevations. The results of our exploratory analysis show the potential that continent-wide ringing databases offer to describe patterns of phenotypic variation along environmental gradients.     

Static intraspecific allometry of the dentition in Otoletnur crassicaudatus

Adult static intraspecific allometry of tooth size was evaluated in a sample of 66 Otolemur crassicaudatus (34 male, 32 female). Tooth areas were calculated from mesiodistal and buccolingual measurements of canines and postcanine teeth of both arcades and were scaled to four viscerocranial measurements: bimaxillary width; maxillo-alveolar length; mandibular length and bigonial width. Individual tooth crown areas were also scaled to total skull length, body length and body weight. From the log-transformed analyses it is concluded that postcanine tooth size was unrelated to body length or weight, and poorly correlated to skull length or jaw size. Although viscerocranial size appears to be independent of body size, these measures are well correlated to skull length. It is shown that the longer the skull, the shorter and narrower the maxilla, and the longer and broader the mandible. Canines are shown to scale negatively allometric to skull length, hence, large animals will have relatively small canines.     

Evolution of multivariate wing allometry in schizophoran flies (Diptera: Schizophora)

The proximate and ultimate mechanisms underlying scaling relationships as well as their evolutionary consequences remain an enigmatic issue in evolutionary biology. Here, I investigate the evolution of wing allometries in the Schizophora, a group of higher Diptera that radiated about 65 million years ago, by studying static allometries in five species using multivariate approaches. Despite the vast ecological diversity observed in contemporary members of the Schizophora and independent evolutionary histories throughout most of the Cenozoic, size‐related changes represent a major contributor to overall variation in wing shape, both within and among species. Static allometries differ between species and sexes, yet multivariate allometries are correlated across species, suggesting a shared developmental programme underlying size‐dependent phenotypic plasticity. Static allometries within species also correlate with evolutionary divergence across 33 different families (belonging to 11 of 13 superfamilies) of the Schizophora. This again points towards a general developmental, genetic or evolutionary mechanism that canalizes or maintains the covariation between shape and size in spite of rapid ecological and morphological diversification during the Cenozoic. I discuss the putative roles of developmental constraints and natural selection in the evolution of wing allometry in the Schizophora.     

Plant allometry, leaf nitrogen and phosphorus stoichiometry, and interspecific trends in annual growth rates

• Background Life forms as diverse as unicellular algae,zooplankton, vascular plants, and mammals appear to obey quarter-powerscaling rules. Among the most famous of these rules is Kleiber's(i.e. basal metabolic rates scale as the three-quarters powerof body mass), which has a botanical analogue (i.e. annual plantgrowth rates scale as the three-quarters power of total bodymass). Numerous theories have tried to explain why these rulesexist, but each has been heavily criticized either on conceptualor empirical grounds. • N,P-Stoichiometry Recent models predicting growth rateson the basis of how total cell, tissue, or organism nitrogenand phosphorus are allocated, respectively, to protein and rRNAcontents may provide the answer, particularly in light of theobservation that annual plant growth rates scale linearly withrespect to standing leaf mass and that total leaf mass scalesisometrically with respect to nitrogen but as the three-quarterspower of leaf phosphorus. For example, when these relationshipsare juxtaposed with other allometric trends, a simple N,P-stoichiometricmodel successfully predicts the relative growth rates of 131diverse C₃ and C₄ species. • Conclusions The melding of allometric and N,P-stoichiometrictheoretical insights provides a robust modelling approach thatconceptually links the subcellular ‘machinery’ ofprotein/ribosomal metabolism to observed growth rates of uni-and multicellular organisms. Because the operation of this ‘machinery’is basic to the biology of all life forms, its allometry mayprovide a mechanistic explanation for the apparent ubiquityof quarter-power scaling rules.     

Interspecific allometry of morphological traits among trematode parasites: selection and constraints

Developmental constraints and selective pressures interact to determine the strength of allometric scaling relationships between body size and the size of morphological traits among related species. Different traits are expected to relate to body size with different scaling exponents, depending on how their function changes disproportionately with increasing body size. For trematodes parasitic in vertebrate guts, the risk of being dislodged should increase disproportionately with body size, whereas basic physiological functions are more likely to increase in proportion to changes in body size. Allometric scaling exponents for attachment structures should thus be higher than those for other structures and should be higher for trematode families using endothermic hosts than for those using ectotherms, given the feeding and digestive characteristics of these hosts. These predictions are tested with data on 363 species from 13 trematode families. Sizes of four morphological structures were investigated, two associated with attachment (oral and ventral suckers) and the other two with feeding and reproduction (pharynx and cirrus sac). The scaling exponents obtained were generally low, the majority falling between 0.2 and 0.5. There were no consistent differences within families between the magnitude of scaling exponents for different structures. Also, there was no difference in the values of scaling exponents between families exploiting endothermic hosts and those using ectotherms. There were strong correlations across families between the values of the scaling exponents for the oral sucker, the ventral sucker and the pharynx: in families where the size of one trait increases relatively steeply as a function of body size, the same is generally true of the other traits. These results suggest either that developmental constraints link several morphological features independently of their specific roles or that similar selection pressures operate on different structures, leading to covariation of scaling exponents. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 96 , 533–540.     

Artificial selection on allometry: change in elevation but not slope

To what extent within-species (static) allometries constitute a constraint on evolution is the subject of a long-standing debate in evolutionary biology. A prerequisite for the constraint hypothesis is that static allometries are hard to change. Several studies have attempted to test this hypothesis with artificial-selection experiments, but their results remain inconclusive due to various methodological issues. Here, we present results from an experiment in which we selected independently on the slope and the elevation of the allometric relationship between caudal-fin size and body size in male guppies (Poecilia reticulata). After three episodes of selection, the allometric elevation (i.e. intercept at constant slope) had diverged markedly between the lines selected to increase or decrease it, and showed a realized heritability of 50%. In contrast, the allometric slope remained unaffected by selection. These results suggest that the allometric elevation is more evolvable than the allometric slope, this latter representing a potential constraint on adaptive trait evolution. To our knowledge, this study is the first artificial-selection experiment that directly tests the evolvability of static allometric slopes.     

Static intraspecific allometry of jaws and teeth in Cercopithecus aethiops

Adult static intraspecific allometry of jaw size and tooth area was evaluated in a sample of 100 Cercopithecus aethiops crania (50 male, 50 female). Tooth areas were calculated from mesiodistal and buccolingual measurements of all the teeth in both arcades and were scaled to four viscero-cranial measurements: bimaxillary breadth, maxillo-alveolar length, mandibular length and bigonial width. Allometric coefficients calculated for jaw dimensions alone indicate tighter viscerocranial integration in females than in males. A finding of note was that half of the variation in maxillo-alveolar length may be accounted for by variation in mandibular length: females are isometric, males negatively allometric.
A similar degree of allometric mosaicism was found when maxillary incisor size was scaled to maxillary length and width. In females, the relationship was negatively allometric, whilst incisor size in males was found to be unrelated to either. Negative allometry characterized the relationship of canine base area to jaw length in both sexes, with males additionally being positively allometric to mandibular width.
The scaling of postcanine tooth areas to jaw length was characterized by a dichotomous pattern: males showed significant mandibular integration whilst females showed only significant maxillary integration. Compensatory tooth size interaction between maxillary canine base area and the summed incisor and postcanine areas was suggested by the significant negative allometric relation between them.     

The origins of allometry: size and shape polymorphism in the common waterstrider, Gerris remigis Say (Heteroptera, Gerridae)

Changes in size, whether ontogenetic or phylogenetic, tend to be associated with changes in shape. This allometry can arise through two different evolutionary mechanisms: (1) selection acting primarily on overall size may be associated with changes in shape because of physiological and mechanical constraints or differential responses of different body components; or (2) selection acting primarily on shape (on the size of specific body components) may be associated with changes in overall size because of genetic correlations, and thus correlated responses, of other body components. To assess the relative importance of these two mechanisms, shape polymorphism is examined along two axes of size dimorphism (sex and wing morphology) in the common waterstrider, Gerris remigis Say. Eight measurements were made of body and appendage components of 234 adults, from three independent populations. Univariate and multivariate analyses reveal that both sexes and wing morphs differ significantly in size and shape. Shape differentiation along the two axes of size dimorphism is found to be dissimilar, partially independent of size, and strongly correlated with the ecological specialization of the various morphs. These observations suggest that selection is acting directly on shape, and thus that allometry in this species primarily reflects shape-mediated changes in size (mechanism 2), rather than size-mediated changes in shape. The role of developmental processes in facilitating this shape differentiation is discussed.     

Skull allometry in the marine toad,Bufo marinus

Scaling predictions pioneered by A.V. Hill state that isometric changes in kinematics result from isometric changes in size. These predictions have been difficult to support because few animals display truly isometric growth. An exception to this rule is said to be the toads in the genus Bufo, which can grow over three orders of magnitude. To determine whether skull shape increases isometrically, I used linear measurements and geometric morphometrics to quantify shape variation in a size series of 69 skulls from the marine toad, B. marinus. Toads ranged in body mass from 1.8 gm to a calculated 1,558.9 gm. Of all linear measurements (S/V length, skull width, skull length, levator mass, depressor mass, adductor foramen area), only the area of the adductor foramen increased faster than body mass; the remaining variables increased more slowly. In addition, modeling the lower jaw as a lever‐arm system showed that the lengths of the closing in‐ and out‐levers scaled isometrically with body mass despite the fact that the skull itself is changing allometrically. Geometric morphometrics discerned areas of greatest variability with increasing body mass at the rear of the skull in the area of the squamosal bone and the adductor foramen. This increase in area of the adductor foramen may allow more muscle to move the relatively greater mass of the lower jaw in larger toads, although adductor mass scales with body mass. If B. marinus feeds in a similar manner to other Bufo, these results imply that morphological allometry may still result in kinematic isometry. J. Morphol. 241:115–126, 1999. © 1999 Wiley‐Liss, Inc.     

Ontogenetic and interspecific organ weight allometry in Old World monkeys

The importance of allometry as an analytic tool is well recognized in the literature of primate morphology. However, a number of recent studies have illustrated how interpretive difficulties can arise when researchers confound different types of allometric data. Such confusion is due less to carelessness than to uncertainty about how different types of allometry are related. The present study examines the relationship between two types—ontogenetic and interspecific allometry–in the case of organ weight scaling in six species of Old World monkeys. Accepting the interpretation of interspecific allometry as a reflection of functional scaling constraints, the results of this analysis indicate how ontogenetic patterns have been modified in different-sized species to maintain compliance with these constraints. Specifically, for the heart and lungs it appears that vertical transpositions of individual species' ontogenies are dictated by isometric interspecific allometry, while in the case of the kidneys and liver, the relation of negative allometry across species entails alteration of the relative growth coefficients of the individual species. While these conclusions can at present only be applied to organ weight scaling, the approach of examining interspecific patterns in light of developmental differences between species should prove very helpful in our efforts to understand the phenomena of size and scaling.     

Walk the line: 600000 years of molar evolution constrained by allometry in the fossil rodent Mimomys savini

The allometric-constraint hypothesis states that evolutionary divergence of morphological traits is restricted by integrated growth regulation. In this study, we test this hypothesis on a time-calibrated and well-documented palaeontological sequence of dental measurements on the Pleistocene arvicoline rodent species Mimomys savini from the Iberian Peninsula. Based on 507 specimens representing nine populations regularly spaced over 600 000 years, we compare static (within-population) and evolutionary (among-population) allometric slopes between the width and the length of the first lower molar. We find that the static allometric slope remains evolutionary stable and predicts the evolutionary allometry quite well. These results support the hypothesis that the macroevolutionary divergence of molar traits is constrained by static allometric relationships.     

Rodlet cell biometry: interspecific and intraspecific variability

Intraspecific and interspecific variability in rodlet cell size in various tissues of several species of freshwater and marine fish were documented. Differences were attributed mainly to fish species, although tissue type contributed significantly, providing evidence for the presence of rodlet cell morphotypes.     

Evolution of ontogeny in the hippopotamus skull: using allometry to dissect developmental change

Allometry describes the effect of size change on aspects of an organism's form and can be used to summarize the developmental history of growing parts of an animal. By comparing how allometric growth differs between species, it is possible to reveal differences in their pathways of development. The ability to compare and categorize developmental change between species is demonstrated here using morphometric methods. This involves the interspecific statistical comparison of a large number of bivariate relationships that summarize ontogenetic trajectories. These linear ontogenetic trajectories can be modified as they evolve in any of three ways: ontogenetic scaling indicative of change in the duration of growth, lateral shifts indicative of changes in prenatal development, and directional change indicative of novel modes of postnatal growth. I apply this analysis to skulls of the common hippopotamus ( Hippopotamus amphibius ) and the pygmy hippopotamus ( Hexaprotodon liberiensis ). The number of allometric changes falling into each category was statistically determined and Jolicoeur's multivariate generalization of simple allometry was used to provide an overview of cranial variation. For these skulls, directional change was not found to be statistically significant, but ontogenetic scaling and lateral shifts were both common. This indicates that conserved patterns of growth covariance (ontogenetic scaling) can be separated from novel or derived patterns (directional change and/or lateral shifts). This study demonstrates that He. liberiensis is not simply an ontogenetically scaled version of its larger relative. The evolutionary implications of allometric growth variation are discussed in the light of these findings and those of other studies.  © 2003 The Linnean Society of London, Biological Journal of the Linnean Society , 2003, 80 , 625–638.     

Fitting statistical models in bivariate allometry

Several attempts have been made in recent years to formulate a general explanation for what appear to be recurring patterns of allometric variation in morphology, physiology, and ecology of both plants and animals (e.g. the Metabolic Theory of Ecology, the Allometric Cascade, the Metabolic‐Level Boundaries hypothesis). However, published estimates for parameters in allometric equations often are inaccurate, owing to undetected bias introduced by the traditional method for fitting lines to empirical data. The traditional method entails fitting a straight line to logarithmic transformations of the original data and then back‐transforming the resulting equation to the arithmetic scale. Because of fundamental changes in distributions attending transformation of predictor and response variables, the traditional practice may cause influential outliers to go undetected, and it may result in an underparameterized model being fitted to the data. Also, substantial bias may be introduced by the insidious rotational distortion that accompanies regression analyses performed on logarithms. Consequently, the aforementioned patterns of allometric variation may be illusions, and the theoretical explanations may be wide of the mark. Problems attending the traditional procedure can be largely avoided in future research simply by performing preliminary analyses on arithmetic values and by validating fitted equations in the arithmetic domain. The goal of most allometric research is to characterize relationships between biological variables and body size, and this is done most effectively with data expressed in the units of measurement. Back‐transforming from a straight line fitted to logarithms is not a generally reliable way to estimate an allometric equation in the original scale.